Monday, July 9, 2007

N Moderation

There are reasons to suspect that science and engineering took a very different path over there: their limited understanding of nuclear weapons—they seem to think that nukes are roughly as easy to build as bottle rockets—suggests that nuclear fission may never have been developed on their timeline.Twilight Zone by Gregory Cochran, on evidence that members of the Bush Administration are from a parallel universe.

Just how hard is it to build a nuke? And what is the smallest amount of plutonium needed to build one?

The smallest nuclear weapon ever designed was the Davy Crockett, aka the W54 warhead, weighing 51 pounds with a variable yield supposedly from 10 to 250 tons of TNT equivalent. It was the last weapon ever atmospheric-tested by the U.S. and in its two tests, (Little Feller I and II) it yielded 22 and 18 tons of explosive power. At those yields, however, the explosive power was pretty much unimportant compared to the radiation the blast produced, lethal to 50% of unshielded personnel at 400 meters, 100% lethal at 300 meters.

There’s not a lot of unclassified information about the actual design of the W54, but some conjectures can be made about it just from the nature of the nuclear chemistry involved. A “bare critical” mass of plutonium, for example, weighs roughly 10 kg, but a neutron reflector reduces this by maybe a factor of two. A uranium reflector/tamper can also increase yield because some fast fission will take place in the reflector itself (at the cost of a time delay in the return of the neutrons to the explosive core). Beryllium also multiplies neutrons, undergoing “light fission” on exposure to high-energy particles of any kind, including neutrons, to produce, well, more neutrons. This is also at the expense of slowing the neutrons and thus retarding the rapid increase in neutron population that make a bomb go ka-boom.

But slowing neutrons is called “moderation” and slower neutrons tend to react more easily with nuclei (have a higher capture cross section) than fast neutrons. This is a consequence of quantum mechanics, where fast particles have a more certain position than do slow ones. Think of the slow neutrons as being more “fuzzy,” virtually bigger, if you will. So if there is a nearby nucleus that is “sticky” for neutrons, a slow neutron is more likely to glom onto it.

That is pretty much the principle of nuclear reactors, where neutrons are slowed down to better react with the fissile elements in the reactor. A mass that is sub-critical for fast neutrons can be more than critical for slow neutrons.

The result is that, with a thick beryllium reflector, the critical mass of normal plutonium can be reduced to less than 20% of its “bare” critical number. The thickness of the reflector in the Davy Crockett was probably dictated by the limit that is reached when adding more reflector increases the overall mass of the design rather than reducing it.

The variable yield of the W54 looks like a signature of a variable fusion boost, but I’ve seen statements to the effect that D-T fusion doesn’t get going until you reach the 100 ton range, so the W54 may have had multiple fission core compositions. Still, the upper limit of the W54 is within the fusion boosting range, so a design modification could possibly have boosted its potential yield to a full kiloton.

A reasonable question arises, is the implied 2 kg core the minimum amount of plutonium (or U233, which has a bare critical mass of about 16 kg) that can be used to make a nuclear weapon, even one of such a low yield as the W54?

Advanced implosion techniques can produce such high core densities that the critical mass for plutonium can be reduced to as little as 1 kilogram, but the tradeoff is a much more complicated design. Besides, if we’re talking terrorists or a small belligerent state with limited technical resources, we’re much more concerned with basement bomb makers, aren’t we? What’s the least amount of bomb grade stuff necessary to be dangerous?

In one sense, the answer is…none. Nuclear reactors can be made from materials that are not considered bomb grade material. There was a nuclear accident in Japan a few years ago that occurred when workers added water (a moderator) to some highly enriched uranium and accidentally produced a critical excursion. The HEU was only 20% U-235, which is considered far below bomb grade, and there was only 35 kilograms of material involved. Nevertheless, the radiation release killed several workers and put an entire town into panic mode.

Ordinary reactor fuel, on the order of 7% U-235 could also serve as a terror weapon, especially if it were moderated by heavy water, which, unlike light water, does not absorb neutrons very effectively. However, hundreds of kilograms of such fuel would be needed.

Suppose, however, that a hypothetical bad guy had some amount of plutonium, just not enough to build a “conventional” nuclear bomb. How much would he need to cause some havoc?

Based on various published figures, plus some conjectures from reactor design principles, I guesstimate that a “prompt critical” device could be built from as little as 50 grams of plutonium, though you’d also need on the order of several hundred kilograms of natural uranium for a reflector/tamper, and a substantial amount of heavy water. Both of those components, however, are relatively easy to procure, although you might need a cover story to get them (maybe a potter with a hobby of trying to build a cold fusion device). In any event, the tamper/casing of the bomb could be produced from materials that one can obtain within the United States; no smuggling would be required. The explosive yield of such a device could be anywhere from a few pounds of TNT up to something approaching the Davy Crockett. In all cases the local radiation would be lethal to some distance, with significant fission product contamination. A full Davy Crockett yield could almost certainly bring down a building or two; the Oklahoma City bomb was about 2 tons in yield, 10% of the Davy Crockett.

Obtaining plutonium, of course, is a difficult matter, but it’s sobering to realize how much MOX (mixed oxide) fuel is around and about, not to mention the fact that waste nuclear fuel rods become less dangerous with each passing year. We’ve already gone through almost two half lives of the most dangerous intermediate isotopes (cesium and strontium). The rule of thumb is that ten half-lives is sufficient for a radiation source to become safe. That reduces the radiation by a factor of 1000. For intermediate fission products, that is about 300 years; 240 now that we’ve passed the first two half-lives, and the spent fuel is now only ¼ as reactive as it was in 1950.

Some fuel rods have been or will be buried in what is called “geological storage” or, as I like to call them, future plutonium mines.

2 comments:

Anonymous said...

Existing there any poofs of the fission nature of the W54??!!
What if the W54 the successor of the netherexisting german uranium-bomb was? Poket bombs are pure fusion bombs, arn't there?

Anonymous said...

You have made several mistakes about the physics and numbers. The "Bare" criticle mass of ploot is about 9 kilos for a conventional early type bomb like those tested by every single national program. (Except for the N. Koreans, possably?) Reflector-tampers required. To get to smaller pits, higher compression was required. The highest possable compression could theoreticly yeald a working bomb with only 2-400 grams of ploot.
The W54 was made in several marks with yealds between ~20 and 1,500 tonnes of TNT. This was set durring manufacture and was a function of efficiancy of the compression, not mass of the core.